// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
/*
This is an example illustrating the use of the kernel ridge regression
object from the dlib C++ Library.
This example will train on data from the sinc function.
*/#include<iostream>#include<vector>#include<dlib/svm.h>usingnamespace std;
usingnamespace dlib;
// Here is the sinc function we will be trying to learn with kernel ridge regression
doublesinc(double x){if(x ==0)return1;
returnsin(x)/x;
}intmain(){// Here we declare that our samples will be 1 dimensional column vectors.
typedef matrix<double,1,1> sample_type;
// Now sample some points from the sinc() function
sample_type m;
std::vector<sample_type> samples;
std::vector<double> labels;
for(double x =-10; x <=4; x +=1){m(0)= x;
samples.push_back(m);
labels.push_back(sinc(x));
}// Now we are making a typedef for the kind of kernel we want to use. I picked the
// radial basis kernel because it only has one parameter and generally gives good
// results without much fiddling.
typedef radial_basis_kernel<sample_type> kernel_type;
// Here we declare an instance of the krr_trainer object. This is the
// object that we will later use to do the training.
krr_trainer<kernel_type> trainer;
// Here we set the kernel we want to use for training. The radial_basis_kernel
// has a parameter called gamma that we need to determine. As a rule of thumb, a good
// gamma to try is 1.0/(mean squared distance between your sample points). So
// below we are using a similar value computed from at most 2000 randomly selected
// samples.
constdouble gamma =3.0/compute_mean_squared_distance(randomly_subsample(samples, 2000));
cout << "using gamma of " << gamma << endl;
trainer.set_kernel(kernel_type(gamma));
// now train a function based on our sample points
decision_function<kernel_type> test = trainer.train(samples, labels);
// now we output the value of the sinc function for a few test points as well as the
// value predicted by our regression.
m(0)=2.5; cout <<sinc(m(0))<< "" <<test(m)<< endl;
m(0)=0.1; cout <<sinc(m(0))<< "" <<test(m)<< endl;
m(0)=-4; cout <<sinc(m(0))<< "" <<test(m)<< endl;
m(0)=5.0; cout <<sinc(m(0))<< "" <<test(m)<< endl;
// The output is as follows:
//using gamma of 0.075
// 0.239389 0.239389
// 0.998334 0.998362
// -0.189201 -0.189254
// -0.191785 -0.186618
// The first column is the true value of the sinc function and the second
// column is the output from the krr estimate.
// Note that the krr_trainer has the ability to tell us the leave-one-out predictions
// for each sample.
std::vector<double> loo_values;
trainer.train(samples, labels, loo_values);
cout << "mean squared LOO error: " <<mean_squared_error(labels,loo_values)<< endl;
cout << "R^2 LOO value: " <<r_squared(labels,loo_values)<< endl;
// Which outputs the following:
// mean squared LOO error: 8.29575e-07
// R^2 LOO value: 0.999995
// Another thing that is worth knowing is that just about everything in dlib is serializable.
// So for example, you can save the test object to disk and recall it later like so:
serialize("saved_function.dat")<< test;
// Now let's open that file back up and load the function object it contains.
deserialize("saved_function.dat")>> test;
}